System and method for data analysis in quantitative pcr measurements

ABSTRACT

Embodiments of the present invention relate to a system and method for determining quantity of target nucleic acid sequence in a sample. During a PCR-based amplification reaction, fluorescence intensity signals are acquired that form an amplification profile from which an exponential amplification region is desirably identified. In determining the exponential region, embodiments of the present invention determine a fluorescence threshold by background subtraction, test the feasibility of matching a signal to a reference curve and, in the event the feasibility test is successful, determine the matching parameters that quantify the initial amplicon number, and signal detection that reduces systematic errors in the measurements and increase the sensitivity of the measurement by decreasing the apparent noise-floor.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority from U.S. ProvisionalPatent Application Ser. No. 63/043,310, filed on Jun. 17, 2020, thedisclosure of which is incorporated herein by reference.

STATEMENT REGARDING FEDERAL RIGHTS

The invention described herein was made with United States Governmentsupport from the National Institute of Standards and Technology (NIST),an agency of the United States Department of Commerce. The United StatesGovernment has certain rights in the invention.

FIELD OF THE INVENTION

The present invention relates generally to nucleic acid analysis, andmore particularly, to a system and method for evaluating resultsobtained from quantitative amplification reactions.

BACKGROUND OF THE INVENTION

Quantitative polymerase chain-reaction (qPCR) measurements are amainstay diagnostic tool for early disease detection. qPCR techniqueinvolves iterating or “cycling” a PCR reaction to double the amount of atarget DNA segment in a sample and detecting fluorescence emissionsignals corresponding to new copy of target DNA generated during eachcycle of the PCR reaction. For example, qPCR can be used to detect viralparticles in a patient sample by targeting a specific genetic sequenceassociated with the viral genome and exponentially amplifying thecorresponding DNA, which is observed indirectly via the increasingamplitude of fluorescence. Fluorescent emission signals are generallynot detected until the concentrations of the duplicated target DNA reachcertain levels and standard amplification protocols of about 40 cyclesprovide sufficient concentrations to detect a single target DNA strand.Further, fluorescence emission signal measurements must account forbackground sources of light that obscure signals of interest.

Typical approaches for the analysis of data obtained from qPCRmeasurements rely on local empirical fits of the amplification curves atlow cycle numbers that are generally before the onset of exponentialgrowth. This assumes that the local behavior can be extrapolated to highcycle numbers to model the global background structure. However, currenttechniques to subtract background signals from qPCR measurement signalsinclude empirical polynomial models that are often extrapolated tocorrect data outside the fit region. Such techniques have been found tointroduce systematic errors into measurements and may decrease thesensitivity of diagnostic protocols by increasing the apparentnoise-floor. This problem is further compounded by data analysistechniques that rely on subjective thresholds that an amplificationcurve (as a function of cycle number) must surpass to be considered atrue positive signal and assumptions that baseline corrections soextracted will be valid for high cycle numbers. Because these thresholdsmust be significantly larger than the apparent noise-floor, systematicerrors unnecessarily force thresholds higher and increase theprobability of false-negatives. Moreover, threshold-based analysismethods do not directly test that the signal manifests exponentialgrowth and, in extreme cases, systematic background errors may lead tofalse positives. Even if the background signals are correctlysubtracted, thresholds may still be unable to detect noisy butstatistically significant signals.

Accordingly, there is a need for an improved method for analyzing datagenerated by qPCR measurements to detect low initial concentrations oftarget nucleic acid while improving the quantitative accuracy andreproducibility of the analysis. There is also a need for a baselinesubtraction technique in qPCR measurements that avoids the use ofempirical models by directly leveraging the behavior of appropriatecontrol experiments. Moreover, there is also need for methods that canidentify mutated strains of variants without the need for full geneticsequencing.

SUMMARY OF THE INVENTION

Embodiments of the present invention relate to a system and method fordetermining quantity of target nucleic acid sequence in a sample.Embodiments of the present invention also relate to methods foridentifying and determining initial quantity of target amplicon in asample. During a PCR-based amplification reaction, fluorescenceintensity signals are acquired that form an amplification profile fromwhich an exponential amplification region is desirably identified. Indetermining the exponential region, embodiments of the present inventiondetermine a fluorescence threshold by background subtraction, test thefeasibility of matching a signal to a reference curve and, in the eventthe feasibility test is successful, determine the matching parametersthat quantify the initial amplicon number, and signal detection thatreduces systematic errors in the measurements and increase thesensitivity of the measurement by decreasing the apparent noise-floor.

Accordingly, embodiments of the present invention relate to a method fordetermining a quantity of a target nucleic acid in a sample, the methodcomprising performing a first amplification reaction on a plurality ofcontrol samples; receiving a plurality of first optical signals as afunction of a first cycle number for the plurality of the controlsamples, wherein the plurality of the first optical signals comprises aplurality of first background signals; performing a second amplificationreaction on the sample; receiving a plurality of second optical signalsas a function of a second cycle number for the target nucleic acid inthe sample, wherein the plurality of the second optical signals compriseat least one of the plurality of the first background signals and aplurality of second background signals; optimizing, using a processor,the plurality of the first background signals from the plurality of thefirst optical signals for each of the plurality of the control samples,wherein the optimizing the plurality of the first background signalscomprises subtracting the plurality of the first background signals fromthe plurality of the second optical signals received to obtain a meanbaseline, wherein the mean baseline corresponds to the second cyclenumber such that the plurality of the second optical signals correspondsto a predetermined value; validating, using the processor, each of theplurality of the second optical signals against at least one of aplurality of reference amplification curves; and computing, using theprocessor, the quantity of the target nucleic acid in the sample fromthe validated plurality of the second optical signals obtained as thefunction of the second cycle number for the target nucleic acid in thesample, wherein computing the quantity of the target nucleic acid in thesample from the validated plurality of the second optical signalscomprises performing an affine transformation to apply at least one of alinear transformation and a translation on the validated plurality ofthe second optical signals. More particularly, the control sample is anextraction blank or a non-template control. In one embodiment of thepresent invention, the sample is a pre-amplified DNA sample. In anotherembodiment of the present invention, the sample is a pre-amplified RNAsample.

In one embodiment of the present invention, the receiving the pluralityof the first optical signals as the function of the first cycle numbercomprises detecting the plurality of the first optical signals for eachof the plurality of the control samples at each cycle of the firstamplification reaction, wherein each cycle of the first amplificationreaction corresponds to the first cycle number; and plotting theplurality of the first optical signals detected as the function of thefirst cycle number for each of the plurality of the control samples toobtain a first amplification curve, wherein the first amplificationcurve represents a ratio of each of the plurality of the first opticalsignals to a passive reporter dye optical signal as the function of thefirst cycle number.

In another embodiment of the present invention, the receiving theplurality of the second optical signals as the function of the secondcycle number comprises detecting the plurality of the second opticalsignals for the target nucleic acid in the sample at each cycle of thesecond amplification reaction, wherein each cycle of the secondamplification reaction corresponds to the second cycle number; andplotting the plurality of the second optical signals detected as thefunction of the second cycle number for the target nucleic acid in thesample to obtain a second amplification curve, wherein the secondamplification curve represents a ratio of each of the plurality of thesecond optical signals to a passive reporter dye optical signal as thefunction of the second cycle number.

In one embodiment of the present invention, the validating each of theplurality of the second optical signals against the at least one of theplurality of the reference amplification curves comprises: generating atleast the one of the plurality of the reference amplification curves,wherein the at least one of the plurality of the reference amplificationcurves comprises a plurality of third optical signals corresponding to areference sample, wherein the at least one of the plurality of thereference amplification curves comprises the plurality of the thirdoptical signals corresponding to a background region, an exponentialgrowth region, and a plateau region; projecting each of the plurality ofthe second optical signals on to the at least one of the plurality ofthe reference amplification signals, wherein the projecting each of theplurality of the second optical signals on to the at least one of theplurality of the reference amplification curves comprises determiningwhether each of the plurality of the second optical signals obtained asthe function of the second cycle number for the target nucleic acid inthe sample collapses on to the at least one of the plurality of thereference amplification curves; and determining a threshold value forthe plurality of the second optical signals projected on to the at leastone of the plurality of the reference amplification curves.

In some embodiments, the validating each of the plurality of the secondoptical signals against the at least one of the plurality of thereference amplification curves further comprises plotting the pluralityof the second optical signals projected on to the at least one of theplurality of the reference amplification curves to obtain a validatedreference amplification curve.

Some embodiments of the present invention further include detecting theplurality of third optical signals for a plurality of amplicons, whereineach of the plurality of the third optical signals correspond to anoptical signal from at least one fluorescent dye.

In one embodiment of the present invention, the linear transformationincludes scaling, and the translation is selected from a groupcomprising a horizontal shift and a vertical scaling.

In another embodiment of the present invention, the validating each ofthe plurality of second optical signals against at least one of aplurality of reference amplification curves includes generating theplurality of the reference amplification curves, wherein each of theplurality of the reference amplification curves comprises a plurality ofthird optical signals corresponding to a reference sample, wherein eachof the plurality of the reference amplification curves comprises theplurality of the third optical signals corresponding to a backgroundregion, an exponential growth region, and a plateau region; projectingthe plurality of the second optical signals onto the plurality of thereference amplification curves, wherein projecting the plurality of thesecond optical signals onto the plurality of the reference amplificationcurves comprises determining whether each of the plurality of the secondoptical signal obtained as the function of the second cycle number forthe target nucleic acid in the sample collapses on to at least one ofthe plurality of reference amplification curves; and determining athreshold value for the plurality of the second optical signalsprojected on to the at least one of the plurality of the referenceamplification curves.

Some embodiments of the present invention further include normalizingthe plurality of the first optical signals and the plurality of thesecond optical signals, wherein normalizing the plurality of the firstand the second optical signals comprises determining a ratio of each ofthe plurality of the first and the second optical signals to a passivereporter dye optical signal.

Another embodiment of the present invention relates to a method fordetermining a quantity of a target nucleic acid in a sample, includingperforming a first amplification reaction on a plurality of controlsamples; receiving a first amplification curve representing a pluralityof first optical signals as a function of a first cycle number for eachof the plurality of control samples at each cycle of the firstamplification reaction, wherein the plurality of the first opticalsignals comprises a plurality of background signals; performing a secondamplification reaction on the sample; receiving a second amplificationcurve representing a plurality of second optical signals as a functionof a second cycle number for the target nucleic acid in the sample ateach cycle of the second amplification reaction; optimizing, using theprocessor, the plurality of the background signals from the receivedplurality of first optical signals for each of the plurality of thecontrol samples, wherein the optimizing the plurality of the backgroundsignals comprises subtracting the plurality of the background signalsfrom the plurality of the second optical signals received to obtain amean baseline, wherein the mean baseline corresponds to the second cyclenumber such that the plurality of the second optical signals correspondsto a predetermined value; validating, using the processor, each of theplurality of second optical signals detected against a plurality ofreference amplification curves, wherein validating each of the pluralityof the second optical signals includes: receiving the plurality of thereference amplification curves, wherein each of the plurality of thereference amplification curves comprises a plurality of third opticalsignals corresponding to a reference sample, wherein each of theplurality of the reference amplification curves comprises the pluralityof the third optical signals corresponding to a background region, anexponential growth region, and a plateau region; projecting each of theplurality of the second optical signals on to the plurality of thereference amplification curves; and determining a threshold for theplurality of the second optical signals projected onto at least one ofthe plurality of the reference amplification curves; and performing,using the processor, an affine transformation on the validated pluralityof the second optical signals to determine the quantity of the targetnucleic acid in the sample, wherein the affine transformation comprisesat least one of a linear transformation and a translation. Moreparticularly, the control sample is an extraction blank or anon-template control. In one embodiment of the present invention, thesample is a pre-amplified DNA sample. In another embodiment of thepresent invention, the sample is a pre-amplified RNA sample.

In some embodiments of the present invention, the projecting each of theplurality of the second optical signals on to the plurality of thereference amplification curves includes determining whether each of theplurality of the second optical signal obtained as the function of thesecond cycle number for the target nucleic acid in the sample collapseson to at the least one of the plurality of the reference amplificationcurves.

Embodiments of the present invention also relate to a system ofdetermining quantity of a target nucleic acid in a sample, including areaction chamber for performing a first amplification reaction on aplurality of control samples and a second amplification reaction on thesample; a detector for detecting a plurality of first optical signals asa function of a first cycle number for the plurality of the controlsamples at each cycle of the first amplification reaction and aplurality of second optical signals as a function of a second cyclenumber for the target nucleic acid in the sample at each cycle of thesecond amplification reaction, wherein the plurality of the firstoptical signals comprises a plurality of background signals; and aprocessor comprising a memory for implementing program instructions of acomputer-readable medium, wherein said program instructions include:optimizing the plurality of the background signals from the receivedplurality of the first optical signals for each of the plurality of thecontrol samples, wherein the optimizing the plurality of the backgroundsignals comprises subtracting the plurality of the background signalsfrom each of the plurality of the second optical signals received toobtain a mean baseline, wherein the mean baseline corresponds to thesecond cycle number such that the plurality of the second opticalsignals correspond to a predetermined value; validating each of theplurality of the second optical signals detected against a plurality ofreference amplification curves, wherein the validating each of theplurality of the second optical signals comprises projecting each of theplurality of the second optical signals on to the plurality of thereference amplification curves to determine a threshold for theplurality of the second optical signals; and computing an initialquantity of the target nucleic acid in the sample from the validatedplurality of the second optical signals obtained as the function of thesecond cycle number for the target nucleic acid in the sample, whereincomputing the initial quantity of the target nucleic acid in the samplefrom the validated plurality of the second optical signals comprisesperforming an affine transformation on the validated plurality of thesecond optical signals, wherein the affine transformation comprises atleast one of a linear transformation and a translation.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a flowchart illustrating an overview of a data analysis methodin accordance with an embodiment of the present invention.

FIG. 2 illustrates an exemplary plot showing fluorescence emissionsignal intensities as a function of cycle number for a PCR reaction.

FIG. 3 illustrates an exemplary plot showing fluorescence emissionsignal intensities as a function of cycle number for extraction blanksor non-template controls.

FIG. 4 illustrates an embodiment of a method for validating fluorescenceemission signal intensities against a reference amplification signalwherein constrained optimization compares a test signal to a referenceor “master” amplification curve.

FIG. 5 illustrates an exemplary analysis applied to RT-qPCR measurementsof N1 fragment of a SARS-CoV-2 RNA construct using methods in accordancewith embodiments of the present invention.

FIG. 6 illustrates exemplary data collapse using optimization methods inaccordance with an embodiment of the present invention.

FIG. 7 illustrates differences between reference and transformed curvesfor the collection of datasets shown in FIG. 6.

FIG. 8 illustrates a plot including truncated data used to test forfeasibility of data collapse using a lower threshold.

FIG. 9 illustrates data collapse of the amplification curves shown inFIG. 8.

FIG. 10 illustrates exemplary transformations of non-template controldata for τ=0 (low-threshold) and τ=μ+5σ (high-threshold), where σ wascomputed individually for each non-template control.

FIG. 11 illustrates feasibility of transforming amplification curves andnon-template controls as a function of the mean threshold τ.

FIG. 12 illustrates the results of affine analysis performed onexemplary datasets spanning 3.5 years.

FIG. 13 illustrates an exemplary analysis applied to RT-qPCRmeasurements of N2 fragment of a SARS-CoV-2 RNA construct using methodsin accordance with embodiments of the present invention and a comparisonof measurements of N2 fragment of a SARS-CoV-2 RNA construct withmeasurements of N1 fragment of a SARS-CoV-2 RNA construct.

FIG. 14 illustrates an exemplary system for performing quantitative PCRin conjunction with the quantitation method in accordance withembodiments of the present invention.

DETAILED DESCRIPTION

While the making and using of various embodiments of the presentinvention are discussed in detail below, it should be appreciated thatthe present invention provides many applicable inventive concepts whichcan be embodied in a wide variety of specific contexts. The specificembodiments discussed herein are merely illustrative of specific ways tomake and use the invention, and do not delimit the scope of the presentinvention. Reference will now be made to the drawings wherein likenumerals refer to like elements throughout.

Referring now to the drawings, and more particularly, to FIG. 1, thereis shown a method for determining quantity of target nucleic acid in abiological sample, generally designated 100, which comprises embodimentsof the present invention.

As used herein, a nucleic acid “sequence” means a nucleic acid basesequence of a polynucleotide. Unless otherwise indicated or apparentfrom context, bases or sequence elements are presented in the order 5′to 3′ as they appear in a polynucleotide.

A “polynucleotide” or “nucleic acid” includes any form of RNA or DNA,including, for example, genomic DNA; complementary DNA (cDNA), which isa DNA representation of messenger RNA (mRNA), usually obtained byreverse transcription of mRNA; and DNA molecules produced syntheticallyor by amplification. Polynucleotides include nucleic acids comprisingnon-standard bases (e.g., inosine). A polynucleotide in accordance withthe invention will generally contain phosphodiester bonds, although insome cases, nucleic acid analogs may be used that may have alternatebackbones, comprising, e.g., phosphoramidate, phosphorothioate,phosphorodithioate, or O-methylphophoroamidite linkages; positivebackbones; non-ionic backbones, and non-ribose backbones.Polynucleotides may be single-stranded or double-stranded.

As used herein, “amplification” of a nucleic acid sequence has its usualmeaning, and refers to in vitro techniques for enzymatically increasingthe number of copies of a target sequence. Amplification methods includeboth asymmetric methods (in which the predominant product issingle-stranded) and conventional methods (in which the predominantproduct is double-stranded).

The terms “amplicon” and “amplification product” are usedinterchangeably and have their usual meaning in the art. Thegrammatically singular term, “amplicon,” can refer to many identicalcopies of an amplification product. Moreover, reference to an “amplicon”encompasses both a molecule produced in an amplification step andidentical molecules produced in subsequent amplification steps (such as,but not limited to, amplification products produced in subsequent roundsof a PCR amplification). Moreover, the term “amplification” may refer tocycles of denaturation, annealing and extension, and does not requiregeometric or exponential increase of a sequence.

As used herein, “quantitative PCR” or “qPCR” refers to quantitativereal-time polymerase chain reaction (PCR), which is also known as“real-time PCR” or “kinetic polymerase chain reaction.”

A “reagent” refers broadly to any agent used in a reaction, other thanthe analyte (e.g., protein being analyzed). Illustrative reagents for anucleic acid amplification or extension reaction include, but are notlimited to, buffer, metal ions, polymerase primers, template nucleicacid, nucleotides, labels, dyes, nucleases, and the like. Reagents forenzyme reactions include, for example, substrates, cofactors, buffer,metal ions, inhibitors, and activators.

The term “label,” as used herein, refers to any atom or molecule thatcan be used to provide a detectable and/or quantifiable signal. Inparticular, the label can be attached, directly or indirectly, to anucleic acid or protein. Suitable labels that can be attached to probesinclude, but are not limited to, radioisotopes, fluorophores,chromophores, mass labels, electron dense particles, magnetic particles,spin labels, molecules that emit chemiluminescence, electrochemicallyactive molecules, enzymes, cofactors, and enzyme substrates.

As used herein, a “sample” refers to any substance comprising a targetnucleic acid of interest (e.g., a target polynucleotide or a targetpolypeptide). The term “sample” thus can include a sample ofpolynucleotide (genomic DNA, cDNA, RNA) and/or polypeptide such as canbe found in a cell, tissue, bodily fluid, tumor, organ, organism,samples of in vitro cell culture constituents, an environmental sample,or industrial sample (e.g., a commercial food product, an industrialwaste product, and the like). Exemplary bodily fluid includes plasma,serum, spinal fluid, lymph fluid, synovial fluid, urine, tears, stool,external secretions of the skin, respiratory, intestinal andgenitourinary tracts, saliva, blood, and the like.

As used herein, “threshold” or “threshold value” refers to afluorescence signal value required for measurement by a fluorescencedetector.

As used herein, “quantification cycle” or “Cq” refers to the PCR cyclenumber at which a sample's amplification curve intersects a threshold.

As used herein, “extraction blank” or “EB” refers to a negative controlin which water (or a clean swab) is used instead of a sample containcells or DNA and all steps for nucleic acid extraction are performed asif it were a normal sample.

As used herein, “non-template control” or “NTC” refers to all reagentsused in the PCR except the template nucleic acid but including theinternal control.

According to various embodiments, quantitation method 100 commences bycollecting samples and preparing a plurality of extraction blanks atstep 102. In an alternate embodiment of the present invention,quantitation method 100 commences by preparing a plurality ofnon-template controls at step 102. At step 104, qPCR measurements areperformed to obtain fluorescence emission signal intensities as afunction of cycle number for each of the plurality of extraction blanksor non-template controls from step 102. At step 106, qPCR measurementsare performed on a plurality of samples containing a target nucleic acidto obtain fluorescence emission signal intensities as a function ofcycle number for the target nucleic acid in each of the samples.

Conventional qPCR techniques may be used to perform qPCR measurements atstep 106. During a typical qPCR process, amplification of a targettemplate DNA strand proceeds through a series of temperature regulatedcycles using the activity of a thermostable enzyme and a sequencespecific primer set. At an appropriate temperature, the primershybridize to portions of the target DNA strand and the enzymesuccessively adds a plurality of nucleotide bases to elongate the primerwhich results in the production of progeny (daughter) strands. Eachprogeny strand possesses a complementary composition relative to thetarget template strand from which it was derived and can serve as atemplate in subsequent reaction cycles.

When applying quantitative methods to PCR-based technologies afluorescent probe or other detectable reporter construct is incorporatedinto the reaction to provide a means for determining the progress of thetarget template DNA amplification. In the case of a fluorescent probe,the reaction fluoresces in relative proportion to the quantity of DNAproduct produced. The reaction kinetics typically change duringamplification of the target such that the amount of product formed doesnot necessarily increase at a constant rate. The quantity or intensityof fluorescence may then be correlated with the amount of product formedin the reaction. In some embodiments of the present invention, a singlefluorescent probe or other detectable reporter construct is used fordetecting a plurality of amplicons.

FIG. 2 illustrates an exemplary amplification curve for a PCR reaction,where fluorescence intensity values are plotted against cycle number ofthe PCR reaction for which the reaction fluorescence is observed. Theamplification curve typically includes a noise region followed by anexponential region and then by a plateau region, as shown in FIG. 2. Thenoise region typically corresponds to the earlier cycles of thereaction, where the observed fluorescence may be erratic and the amountof fluorescence produced by the amplification reaction cannot be readilydistinguished from background and/or non-specific fluorescence producedby the instrumentation and detection equipment. It is typicallydesirable to distinguish the noise region from other regions of theamplification curve, which may more accurately reflect the truefluorescence of the desired products of the reaction. It is alsotypically desired to normalize the data and determine a baseline that isfit to the data extending through the noise region. The baseline may besubtracted from raw fluorescence data to convert the data into correctedmeasurements of fluorescence intensity. The growth portion reflects theonset of amplification, which occurs at the end of the baseline obtainedusing the noise region. A growth portion may have exponential,sigmoidal, high order polynomial, or other type of logistic function orlogistic curve that models growth.

It is desirable to identify a transition point at the end of thebaseline, which is referred to commonly as the elbow value (where thefluorescence signal begins to increase exponentially) for understandingcharacteristics of the PCR amplification process. After the applicationof a baseline, a quantification cycle value (Cq) may be used as ameasure of efficiency of the PCR process. For example, typically adefined signal threshold is determined for all reactions to be analyzedand the number of cycles (Cq) required to reach this threshold value isdetermined for the target nucleic acid as well as for reference nucleicacids such as a standard or housekeeping gene. The absolute or relativecopy numbers of the target molecule can be determined on the basis ofthe Cq values obtained for the target nucleic acid and the referencenucleic acid.

As shown in FIG. 2, the exponential region may be followed by a plateauregion where the reaction is no longer increasing in an exponentialmanner. Typically, the plateau region occurs in the later cycles of thereaction and results from depletion of primers or reagents. Whenperforming quantitation calculations, it is useful to distinguish theexponential region from the plateau region to avoid erroneous ornon-representative quantitation values. Methods in accordance with thepresent invention as described herein distinguish the noise region fromthe exponential region and the plateau region.

FIG. 3 illustrates an exemplary plot showing fluorescence emissionsignal intensities as a function of cycle number for extraction blanksor non-template controls. For the cycles typically considered to bewithin the noise region (cycles 3 to 15), the curves exhibit anapproximately linear behavior on a logarithmic scale, which correspondsto exponential growth on a linear scale and changes in the regionstypically associated with exponential growth and plateau (cycles 25 to40). When performing background subtraction, it is useful to account forthis change in behavior of the extraction blanks or non-templatecontrols to avoid over- or under-correcting the amplification curves inthe exponential and plateau regions.

As an initial preconditioning step, all fluorescence emission signals,including signals obtained from extraction blanks or non-templatecontrols, obtained are normalized at step 108 so that the maximumfluorescence emission signal intensity of any amplification curve is oforder 1. Normalization of fluorescence emission signals is generallydependent on the amplification chemistry.

In one embodiment of the present invention, normalization offluorescence emission signals can be accomplished by dividing the rawfluorescence emission signal intensities by fluorescence emission signalintensities of a passive reporter dye to obtain a ratio denotingnormalized reporter. A normalized reporter value can be calculated forevery cycle and is typically plotted as an available view of the qPCRamplification data. Exemplary passive reporter dyes that can be used fornormalizing fluorescence emission signals include 6-carboxyl-X-Rhodamine(ROX), carboxytetramethylrhodamine (TAMRA™), a Black Hole Quencher (BHQ)dye, an OREGON GREEN® dye (Molecular Probes),4-dimethylaminoazobenzene-4′-sulfonyl chloride (DAB SYL);tetrachlorofluorescein (TET), and the like. In another embodiment of thepresent invention, normalization of fluorescence emission signals can beaccomplished without a passive reference dye by dividing all signals byan arbitrary constant such that the maximum signals are on the numericalscale of unity.

Measurement signals obtained from extraction blanks at step 104 may beused as background signals for subsequent measurements of samples. Asfurther shown in FIG. 3, fluorescence emission signal intensities as afunction of cycle number for extraction blanks or non-template controlsis non-linear and varies for each of the extraction blank ornon-template control measured. Accordingly, background signals obtainedat step 104 are not subtracted from signals obtained for samples.Instead, background signals obtained from measurements of extractionblanks (or non-template controls) at step 104 are optimized at step 108to determine the amount of background that, when removed from samplesignals obtained at step 106, minimizes the mean baseline and itsvariation. This baseline corresponds to the first few cycles of theamplification curve where there are too few fluorophores to detect.

In one embodiment of the present invention, optimization of backgroundsignals at step 108 can be performed using an approach that leveragesinformation obtained from extraction blanks (or non-template controls).This approach postulates that the fluorescence signal can be expressedin the form

d _(n) =s _(n) +βb _(n) c+η _(n)  (1)

where s_(n) is the “true,” noiseless signal, b_(n) is the average overextraction blank signals (or non-template controls), the β, c areunknown parameters quantifying the amount of systematic backgroundeffects and offset (e.g. due to photodetector dark currents)contributing to the measured signal, and η is zero-mean,delta-correlated background noise; that is, the average overrealizations of η satisfies (η_(n)η_(n)′)=σ²δ_(n,n′), where δ_(n,n′) isthe Kronecker delta and σ² is independent of n.

Next, an objective function of the form shown below is minimized withrespect to 13 and c, which determines optimal values of theseparameters,

$\begin{matrix}{{\mathcal{L}_{b}\left( {\beta,c} \right)} = {{\epsilon\left( {\beta - 1} \right)}^{2} + {\sum_{n = N_{0}}^{N_{h}}\frac{\left( {d_{n} - {\beta b_{n}} - c} \right)^{2}}{{\Delta N} - 1}} + \left\lbrack {\frac{1}{\Delta N}{\sum_{n = N_{0}}^{N_{h}}\left( {d_{n} - {\beta b_{n}} - c} \right)}} \right\rbrack^{2}}} & (2)\end{matrix}$

wherein, ϵ is a regularization parameter satisfying 0<ϵ<<1, ΔN=N_(h)−N0,and N₀ and N_(h) are lower and upper cycles for which s_(n) is expectedto be zero. In one embodiment of the present invention, c is set to10⁻³. N₀ is set to 5 to accommodate transient effects associated withthe first few cycles. N_(h) is determined iteratively by: (i) settingN_(h)=15 and minimizing Eq. (2); (ii) estimating C_(q) as the (integer)cycle closest to a threshold of 0.1; and (iii) defining N_(h) as thenearest integer to C_(q)−z. In an exemplary embodiment of the presentinvention, z is set to 6, which, assuming perfect amplification,corresponds to N_(h) falling within the cycles for which d_(n) isdominated by the noise η_(n). z and the corresponding threshold can bechanged as needed, provided z is large enough to ensure that the abovecriterion is satisfied. Optimization of Eq. (2) amounts to calculatingthe amount of extraction blank signal that, when subtracted from d_(n),minimizes the mean-squared and variance of s_(n) in the region where itis expected to be dominated by the noise η.

Referring to FIG. 1, at step 110, fluorescence emission signalintensities obtained at step 106, as a function of cycle number for thetarget nucleic acid in each of the samples, are validated against areference amplification signal. FIG. 4 illustrates an embodiment of amethod 400 for validating the fluorescence emission signal intensitiesobtained from samples at step 106 against a reference amplificationsignal, wherein constrained optimization compares a test signal to areference or “master” amplification curve. An appropriate referencesample should be considered for accurate quantification of the nucleicacid expression because the quantification cycle (C_(q)) of the targetnucleic acid is compared to the C_(q) of the reference sample.

In one embodiment of the present invention, validation method 400creates a reference or “master” amplification curve at step 402 thatexhibits exponential growth at an early cycle number. In anotherembodiment of the present invention, validation method 400 creates alibrary of reference or master amplification curves at step 402. In someembodiments of the present invention, the library of reference or masteramplification curves may be from a predetermined collection of referencesamples. In some embodiments of the present invention, the referenceamplification curve may include data from all phases of the PCRreaction, including background noise or no detectable signal,exponential growth, and plateau. In other embodiments of the presentinvention, the reference amplification curve is typically a rawmeasurement signal from a non-template control followed by datasmoothing in regions of the data where the exponential phase meets thenoise floor.

In an embodiment in accordance with the present invention, a referencesignal δ is obtained by fitting a cubic spline to the amplificationcurve obtained from a sample with the smallest Cq value determined bysetting the threshold at 0.1. Moreover, comparison of amplificationcurves with initial template numbers that do not differ by multiples ofp requires estimation of δ at non-integer cycles, and some form ofinterpolation. Data fits using cubic splines minimize curvature andexhibit non-oscillatory behavior for the data sets under consideration.Other methods that can be used to fit data include penalized splines(P-splines), restricted cubic splines (RCS), natural splines (NS),fractional polynomials (FP), and the like.

At step 404, validation method 400 applies a constrained optimizationapproach to determine whether an amplification curve exhibitscharacteristics that are representative of a true signal by projectingsample signals data obtained at step 106 onto a reference amplificationcurve obtained at step 402. In one embodiment of the present invention,validation method 400 determines whether each of sample signals obtainedat step 106 can be collapsed to master signal obtained at step 402. Insome embodiments of the present invention, validation method 400 appliesa constrained optimization approach at step 404 to determine whether anamplification curve exhibits characteristics that are representative ofa true signal by projecting sample signals data obtained at step 106onto a library of reference amplification curves to identify a referenceamplification curve having a closest match to the given sample.Fluorescence emission signal intensities obtained at step 106 fromsamples having a particular nucleic acid sequence will only collapseonto a reference amplification signal for the same nucleic acidsequence, i.e. there is amplicon specificity. For example, amplificationcurves obtained for N1 sequence of covid-19 will collapse only on toreference amplification curve obtained using N1 sequence of covid-19 andN2 sequence of covid-19 will collapse only on to reference amplificationcurve obtained using N2 sequence of covid-19, as shown in FIG. 13. FIG.5 illustrates an exemplary analysis applied to RT-qPCR measurements ofthe N1 fragment of a SARS-CoV-2 RNA construct. FIG. 5(A) shows qPCRcurves after background subtraction and FIG. 5(B) shows amplificationcurves after data collapse with the inset showing error on an absolutescale relative to the master curve.

In one embodiment of the present invention, data collapse is validatedusing an objective function of the form

(a,c,k,β)=Σ_(N) _(min) ^(N) ^(max) [δ(n−k)−ad _(n) −c−βb _(n)]²  (3)

wherein a, c, β, and k are unspecified parameters, and N_(min) andN_(max) are indices characterizing the cycles for which d_(n) is abovethe noise floor. Minimizing L with respect to its arguments yields thetransformation that best matches d_(n) onto the reference curve δ(n),wherein δ(n) is an interpolation. In one embodiment of the presentinvention, δ(n) is a cubic spline. The background signal bn is includedin this optimization to ensure that any over or undercorrection of thebaseline relative to d is undone.

The quantity N_(min) is taken to be the last cycle for which d_(n)<μ+3σ,where

$\begin{matrix}\begin{matrix}{µ = {\frac{1}{10}{\sum_{n = 5}^{14}d_{n}}}} & {\sigma^{2} = {\frac{1}{9}{\sum_{n = 5}^{14}\left( {µ - d_{n}} \right)^{2}}}}\end{matrix} & (4)\end{matrix}$

are estimates of the mean and variance associated with the noise η. IfN_(min) was less than or equal to 30, then N_(max) is set to 37; else,N_(max) is set to 40. While it is generally possible to set N_(max) to40 for all data sets, it has been observed in certain scenarios that anamplification curve with a higher nominal C_(q) may saturate faster thanδ In such scenarios, it may be necessary to decrease N_(max) so that theinterval [N_(min), N_(max)] is within the domain of cycles spanned by δExcept in scenarios noted above, a meaningfully change may not beobserved if such restrictions are imposed for all curves with nominalC_(q) values less than or equal to 30.

The objective function of Eq. (7) is minimized subject to the followingconstraints that ensure the solution provides fidelity of the datacollapse.

−3σ−μ≤c≤3σ+μ  (5a)

−3σ−μ·β≤3σ+μ  (5b)

−3σ−μ≤c+β≤3σ+μ  (5c)

a _(min) ≤a≤a _(max)  (5d)

−10≤k≤40  (5e)

τ≤ad _(N) _(max) +c+βb _(N) _(max)   (5f)

|δ(n−k)−ad _(n) −c−βb _(n)|≤

  (5g)

Inequalities shown in Eqs. (5a)-(5c) require that the constant offset,noise correction, and linear combination thereof be within the 99%confidence interval of the noise-floor plus any potential offset in themean (which should be close to zero). Inequality of Eq. (5d) prohibitsthe multiplicative scale factor from adopting extreme values that wouldmake noise appear to be true exponential growth. In one embodiment,a_(min)=0.7 and a_(max)=1.3 when inequality of Eq. (5d) prohibits themultiplicative scale factor from adopting extreme values that would makenoise appear to be true exponential growth. In some embodiments, a rangeof admissible values of a corresponds to the maximum variability in theabsolute number of reagents per well, which is partially controlled bypipetting errors. Inequality shown in Eq. (5e) controls the range ofphysically reasonable horizontal offsets. Eq. (5f) requires that thelast data-point of ad_(Nmax) be above some threshold z, and Eq. (5g)requires that the absolute error between the reference and scaled curvesbe less than or equal to

. In an idealized measurement,

may be set to be equal to 3σ, but in multichannel systems, imperfectionsin demultiplexing and/or inherent photodetector noise can introduceadditional uncertainties that limit resolution. In another exemplaryembodiment of the present invention, inequality show in Eq. (5g) may beexpressed in a differentiable form as two separate inequalities.

The optimal transformation parameters a_(*), c_(*), k_(*), and β_(*)determined by minimizing the objective function represented by Eq. (2)is used to define the transformed signal as represented by Eq. (6).

d _(*)(x)=a _(*) d _(x+k) _(*) +c _(*)+β_(*) b _(x+k) _(*)   (6)

where x+k_(*) is required to be an integer in the interval [N_(min),N_(max)].

FIG. 6 illustrates exemplary data collapse using optimization methods inaccordance with an embodiment of the present invention. FIG. 6(A)illustrates a collection of 43 curves having C_(q) values of less than37 according to a threshold of 0.1. FIG. 6(B) illustrates the data setsshown in FIG. 6(A) after collapse onto the first curve from the left setas the reference amplification curve. In FIG. 6, during optimization ofdata collapse,

is set to be equal to 0:03, which corresponds to roughly 1% of the fullscale of the measurement. FIG. 7 illustrates differences between thereference and transformed curves for the collection of datasets in FIG.6. FIG. 7 illustrates that the errors are less than 0.03 on thenormalized fluorescence scale down to the noise floor. This correspondsto less than 1% disagreement relative to the maximum scale. FIG. 6 andFIG. 7 further demonstrates the validity of Eq. (6) for a collection ofdatasets using a threshold τ=0:05 and having an agreement influorescence values of about 0.01, which is more than a decade belowtypical threshold values used to compute C_(q) for this amplificationchemistry. In some embodiments of the present invention, the validateddata obtained by data projected or collapsed on to the reference curveis plotted to obtain a validated reference amplification curve. Thevalidated referenced can then be added to the library of referenceamplification curves.

At step 406, measurement sensitivity for fluorescence emission signalintensities obtained at step 106 is improved by decreasing fluorescencedetection threshold. Embodiments of method 100 in accordance with thepresent invention recognizes that an advantage of the constrainedoptimization approach used in 404, as specified in Eqs. (3)-(5g), is theability to determine when the data set gives rise to a consistent set ofconstraints. More particularly, inequality shown in Eq. (5g) requiresthat the transformed signal be within a noise-threshold of the referencefor an observable exponential growth.

In an exemplary embodiment of the present invention, data set shown inFIG. 8 is used to demonstrate that a non-empty feasible region of theconstraints provides a necessary and sufficient condition fordetermining which data sets have behavior that can be consideredstatistically meaningful, which in turn can be used to lower thefluorescence thresholds.

In data set of FIG. 8, all data points above a normalized fluorescencevalue of 0.05 are removed. In this exemplary embodiment, a normalizefluorescence value of 0.05 represents a factor of four below theautomated value used by the instrument. The affine transformationaccording to Eqs. (3)-(5g) is repeated for the last six data points andby setting

=3 and τ=,μ+6σ in Eq. (5f). In this exemplary embodiment, the value of

is determined entirely by the noise-floor because a significant spectraloverlap is not anticipated at such low fluorescence values.

FIG. 8 illustrates a plot including truncated data used to test forfeasibility of data collapse using a lower threshold. In FIG. 8, thesolid curve is the master curve and the remaining curves have beentruncated at the last cycle for which they are below a threshold of0.05. FIG. 9 illustrates data collapse of the amplification curves shownin FIG. 8. In FIG. 9, the variation in the data below cycle 15 is anartifact of the logarithmic scale that reflects the magnitude of thebackground noise, and the inset shows that the errors relative to themaster curve are less than 10⁻². Further, in FIG. 9, for fluorescencevalues between 10⁻² and 0.05, the transformed curves are nearlyindistinguishable. As shown in FIG. 9, data collapse is achieved usingthe tightened uncertainty threshold given in terms of the noise-floorand errors relative to the reference curve are less than 0.01 on thenormalized fluorescence scale.

FIG. 10 illustrates exemplary transformations of non-template controldata for τ=0 (low-threshold) and τ=μ+5σ (high-threshold), where σ wascomputed individually for each non-template control. FIG. 10demonstrates that optimization of the transformation parameters does notgenerate false positives when the non-template control datasets arebaseline-corrected using the methods used on the amplification curves inaccordance with an embodiment of the present invention. When τ is small,optimization of transformation parameters maps the non-template controlsinto the background of the reference curve, thereby illustrating therole of inequality shown in (5f). When τ is large, the optimization oftransformation parameters are infeasible, which suggests that there isno transformation satisfying the constraints.

FIG. 11 illustrates feasibility of transforming amplification curves andnon-template controls as a function of the mean threshold r. In FIG. 11,the mean value was estimated by setting τ=μ+nσ for n=1, 2, . . . , 10for each amplification curve and averaging over the correspondingrealizations of τ for a fixed n. This process was repeated separatelyfor the non-template controls, including n=0. Further, FIG. 11 shows theaverage of τ values with one-standard-deviation confidence intervals foreach value of n for the amplification curves. In FIG. 11, a setting of5σ≤τ−μ<8σ yields neither false negatives nor false positives.

Referring back to FIG. 1, output from the data collapse in signalvalidation step at 110 is used to quantify the initial amount of nucleicacid in the sample at step 112. Quantification method at step 112leverages a universal property of qPCR; under general conditions, allamplification curves are the same up to an affine transformation. In anembodiment of the present invention, an affine transformation includes amultiplicative, vertical scaling factor and a horizontal shift. In oneembodiment of the present invention, affine transformation includesapplying affine parameters for a linear transformation and a translationto the data obtained from validation step at 110. Exemplary lineartransformations include vertical scaling. Exemplary translations includehorizontal shift and vertical shift. In another embodiment of thepresent invention, affine transformation includes applying affineparameters represented by a polynomial function of a variable to apply amultiplicative factor and a horizontal shift to the data obtained fromvalidation step at 110.

A framework for quantification method at step 112 is based on a genericformulation of a PCR measurement. In this framework, d_(n) representsthe number of DNA strands at the nth amplification cycle, which, in anoiseless environment, is taken to be proportional to the fluorescencesignal measured by the instrument. The outcome of a completed PCRmeasurement is represented by a vector of the form d=(d₁, d₂, . . . ,d_(N)), where N is the maximum cycle number. It is also assumed thatd=d(x, y) is a function of the initial template copy number x and thenumbers of all other reagents denoted by y.

In one embodiment of the present invention, a framework forquantification method at step 112 requires the following assumptions.First, the framework requires that y be a scalar. This assumptionimplies that there is a single experimental variable (in addition toinitial DNA copies) that controls the progression of the reactions. Thiscondition may be satisfied if all samples to be analyzed include eithera single limiting reagent (e.g. primers) or multiple limiting reagentsin the same relative concentrations.

Second, the framework requires that there be a p>1 such that a p-foldincrease in the initial template number shifts the PCR curve to the leftby one cycle. Within a framework in accordance with embodiments of thepresent invention, such p-fold increase in initial template shift may berepresented by

d _(n-q)(p ^(q) ,y)=d _(n)(1,y)  (7)

In embodiments of the present invention, an increase in template shiftas represented by Eq. (7) only requires the amplification efficiency toremain constant over some initial set of cycles q_(max) corresponding tothe maximum initial template copy number expected in any givenexperimental system. In other embodiments of the present invention, anincrease in template shift is represented by the following.

d _(n-log) _(p) _((q/q′))(q,N)=d _(n)(q′,N)  (8)

A framework for quantification method at step 112 also requires signalgeneration be a linear process. This requirement suggests that (i) eachsample (e.g. in a well-plate) may be considered to include multiplesub-samples such that the relative fractions of initial DNA and reagentsis in proportion to their volumes, and (ii) the total signal generatedby a sample is equal to the sum of signals generated by thesesub-samples as if they had been separated into different wells. Thelinearity assumption due to partitioning of an initial template copy andreagent numbers into sub-samples may be represented by the following forany k>0.

d _(n)(k,kN)=kd _(n)(1,N)  (9)

In alternate embodiments of the present invention, a framework forquantification method at step 112 including two values, (x, y) and (χ,γ), for initial template copy number and the numbers of all otherreagents, may be represented by the following.

$\begin{matrix}\begin{matrix}{{d_{n}\left( {\chi,\gamma} \right)} = {\left( {\gamma/y} \right){d_{n}\left( {{\chi{y/\gamma}},y} \right)}}} \\{= {\left( {\gamma/y} \right){d_{n - {\log_{p}{\lbrack{\chi{y/{({\gamma x})}}}\rbrack}}}\left( {x,y} \right)}}} \\{= {a{d_{n - b}\left( {x,y} \right)}}}\end{matrix} & (10)\end{matrix}$

Eq. (10) suggests that all PCR signals are the same up to amultiplicative factor a=γ/y and horizontal shift b=log_(p)[χy/(χx)] whenabove assumptions are applied, as required by a framework forquantification method at step 112 in accordance with embodiments of thepresent invention. This universal property applies irrespective of theactual shape of the amplification curve and under a few genericassumptions. Further, an amplification efficiency does not play a rolein the above analysis, as suggested in Eq. (10).

Methods in accordance with embodiments of the present invention hasseveral advantages over previous methods for background subtraction anddata analysis. More particularly, method 100 for determining quantity oftarget nucleic acid in a biological sample in accordance withembodiments of the present invention has more flexibility. Morespecifically, the generality of the assumptions underpinning Eq. (10)suggests that a master curve may be useful for characterizing qPCR datairrespective of when or where the data was collected. Such universalityis advantageous because it facilitates transfer of analyses betweenlaboratories without the need to generate independent master curves.Independent master curves could be developed once with the creation ofan assay and used as a type of standard reference data. Such approachescould further harmonize analyses across laboratories and thereby reduceuncertainty in qPCR testing. It has also been discovered that a singlemaster curve can be used for accurate data collapse over measurementsfrom a timeframe spanning a number of years and that the use of a mastercurve is backwards and forward compatible. Moreover, a library ofdifferent master curves can be used to identify a closest match to agiven sample to determine the genetic sequence without the need fordirect sequencing experiments. Failure to collapse to a member of thelibrary can indicate a new genetic strain (e.g. of a virus) or indicatequality control problems with the amplification.

In an exemplary embodiment of the present invention using method 100 fordetermining quantity of target nucleic acid in a biological sample,analyses were performed on 223 datasets collected over 3.5 years fromsamples having the same nucleic acid sequence and amplificationchemistry. A single low C_(q) curve measured was chosen at random fromthis set as a master curve, and data collapse was performed on theremaining 222 using optimization methods represented by Eqs. (3)-(5g).FIG. 12 illustrates the results of affine analysis performed on the 223exemplary datasets spanning 3.5 years. FIG. 12(A) shows 223amplification curves after background subtraction and FIG. 12(B) showsall datasets collapsed onto one of the amplification curves.

The absolute errors after transformation are also shown in FIG. 12(B),which suggests that the data collapse is accurate to within about 1% ofthe full scale for nearly all of the measurements. In the affineanalysis shown in FIG. 12,

is set to 0.04 and the minimum and maximum values of a was set to be 0.1and 3 to account for large variations in peak fluorescence.

Reference now to the specific examples which follow will provide aclearer understanding of systems in accordance with embodiments of thepresent invention. The examples should not be construed as a limitationupon the scope of the present invention.

Example Application to SARS-CoV-2 RNA

A. SARS-CoV-2 RNA Constructs

A method in accordance with an embodiment of the present invention wasapplied to RT-qPCR measurements of the N1 and N2 fragments of SARS-CoV-2RNA. The underlying samples were derived from an in-house, in-vitrotranscribed RNA fragment containing approximately 4000 bases ofSARS-CoV-2 RNA sequence. This non-infectious fragment contains thecomplete N gene and E gene, as well as the intervening sequence.

Neat samples of this material were diluted 1:100, 1:500, 1:1000 and1:1500 in RNA Storage Solution (Thermo Fisher) with 5 ng/μL Jurkat RNA(Thermo Fisher) prior to being run for qPCR. qPCR measurements wereperformed using the 2019-nCoV CDC Assays (IDT). The N1 and N2 targets onthe N gene were measured. Each reaction consisted of 8.5 μL water, 5TaqPath RT-qPCR Master Mix, 1.5 μL of the IDT primer and probe mix foreither N1 or N2, and 5 μL of sample setup in a 96-well optical qCPRplate (Phoenix) and sealed with optical adhesive film (VWR). Aftersealing the plate, it was briefly centrifuged to eliminate bubbles inthe wells. qPCR was performed on an Applied Biosystems 7500 HIDinstrument with the following thermal cycling protocol: 25 degree C. for2 minutes, 50 degree C. for 15 minutes, 95 degree C. for 2 minutesfollowed by 45 cycle of 95 degree C. for 3 seconds and 55 degree C. for30 seconds. Data was collected at the 55 degree C. stage for 30 secondsfor each of the cycles across all wells. Upon completion of every run,data was exported into a spreadsheet for further analysis using Matlab™.

B. Analysis of RT-qPCR Measurements

Data analysis proceeded using non-template controls in lieu ofextraction blanks for the background signal bn. FIG. 5 shows the resultsof this analysis applied to the N1 fragment of a SARS-CoV-2 RNAconstruct. The level of agreement between curves after data collapseconfirms that these signals are virtually identical up to an affinetransformation. FIG. 13 shows analogous results for N2 fragment of aSARS-CoV-2 RNA construct. FIG. 13 also illustrates that it not feasibleto transform the N2 amplification curves onto the N1 master curve in thebottom plot; the N1 master curve is different in shape from its N2counterparts. This demonstrates that while the master curve may betransferable across laboratories, it is still specific to theamplification chemistry and target under consideration.

FIG. 14 illustrates an exemplary system 1400 for performing quantitativePCR in conjunction with the quantitation method in accordance withembodiments of the present invention. In one aspect, the system 1400comprises a reaction module 1402, an optical detection module 1404, acontroller 1406 and a processor 1408, which may be interconnected ornetworked by way of a communications medium to substantially automatethe analysis.

Reaction module 1402 receives the samples and thermally cycles thesamples to precise temperatures to promote nucleotide denaturation,annealing, and then polymerase-mediated extension for each round ofnucleic acid amplification. In one embodiment, reaction module includesa reaction chamber 1402 a coupled to a heating element 1402 b and acooling element 1402 c configured to thermally cycle the sample inthrough controlled heating and cooling steps executed over designatedtime intervals. In one embodiment of the present invention, reactionchamber 1402 a can include a block with plurality of reactions wellshaving a predetermined reaction volume. In one example, a reactionchamber may be a 96-well block with reaction volumes ranging from 1 to125 μl, a 384-well block with reaction volumes in the pico to nanoliterrange. In some embodiments, temperature controller 1406 b uses asolid-state active heat pump that transfers heat from one side ofreaction chamber to the other against a temperature gradient with theconsumption of electrical energy. In other embodiments of the presentinvention, temperature control is achieved by suspending tubes inreaction chambers and circulating air having a predetermined temperaturefor time periods as required for PCR.

Optical detection module 1404 determines the presence of target nucleicacid sequence in the sample by detecting and measuring fluorescencegenerated in the presence of a fluorescent reporter, such as aDNA-binding dye or labeled probe, for each amplification reaction andtransmits the fluorescence data to controller 1406. Optical detectionmodule 1404 can include a wide variety of optics systems that use acombination of light sources, filters, and detectors to measure theamount of fluorescence that is present in the amplification reactions.Exemplary light sources that can be used include light-emitting diodes(LEDs), halogen lamp, laser, and the like. Exemplary detectors that canbe used include a photodiode, a charge coupled device (CCD), aphotomultiplier tube, and the like.

Controller 1406 is coupled to reaction module 1402 and optical detectionmodule 1404, and may be configured to communicate with each module ofthe system and coordinate system-wide activities to facilitate theautomated quantitative PCR analysis. In one embodiment of the presentinvention, controller 1406 is configured to communicate with each moduleof the system for protocol setup, plate setup and data collection.Protocol setup may include specifying the denaturation, annealing, andextension parameters, the number of repeated cycles, and the steps atwhich data are to be collected. Plate setup may include identifying thecontents of each well so that data can be properly analyzed oncecollected and designate the wells to be read.

Controller 1406 incudes a temperature controller 1406 a that is coupledto heating element 1402 b and cooling element 1402 c of reaction module1402 and configured to regulate the temperature of the samples inreaction chamber 1402 a. Controller 1406 incudes a data acquisitionmodule 1406 b to record the fluorescence data for each reaction over thespecified time course. Data acquisition module 1406 b may store the datain numerous different forms and configurations including tables, charts,arrays, spreadsheets, databases, and the like.

Processor 1408 is coupled to controller 1406 to receive fluorescencedata from data acquisition module 1406 b, plots the fluorescenceintensity of the reaction mixture in each well versus the reactioncycle, and performs quantitation method 100 in accordance withembodiments of the present invention. Once a run is complete, processor1408 performs a background subtraction, signal validation and quantifiesthe initial amount of nucleic acid sequence in the sample usingquantitation method 100 in accordance with various embodiments of thepresent invention. Quantitation method 100 may be implemented using oneor more computer program or modules which comprise functions designed tomanipulate the data and generate requested information. In one aspect,the processor 1408 is designed to operate in a user-independent mannerwhere all of the calculations and analytical tasks are performed withoutthe need for the user to manually assess or interpret the data.

Systems and methods for determining quantity of target nucleic acid in abiological sample in accordance with one or more embodiments of thepresent invention can be adapted to a variety of configurations. It isthought that systems and methods for determining quantity of targetnucleic acid in a biological sample in accordance with variousembodiments of the present invention and many of its attendantadvantages will be understood from the foregoing description and it willbe apparent that various changes may be made without departing from thespirit and scope of the invention or sacrificing all of its materialadvantages, the form hereinbefore described being merely a preferred orexemplary embodiment thereof.

Those familiar with the art will understand that embodiments of theinvention may be employed, for various specific purposes, withoutdeparting from the essential substance thereof. The description of anyone embodiment given above is intended to illustrate an example ratherthan to limit the invention. This above description is not intended toindicate that any one embodiment is necessarily preferred over any otherone for all purposes, or to limit the scope of the invention bydescribing any such embodiment, which invention scope is intended to bedetermined by the claims, properly construed, including all subjectmatter encompassed by the doctrine of equivalents as properly applied tothe claims.

What is claimed is:
 1. A method for determining a quantity of a targetnucleic acid in a sample, the method comprising: performing a firstamplification reaction on a plurality of control samples; receiving aplurality of first optical signals as a function of a first cycle numberfor the plurality of the control samples, wherein the plurality of thefirst optical signals comprises a plurality of first background signals;performing a second amplification reaction on the sample; receiving aplurality of second optical signals as a function of a second cyclenumber for the target nucleic acid in the sample, wherein the pluralityof the second optical signals comprise at least one of the plurality ofthe first background signals and a plurality of second backgroundsignals; optimizing, using a processor, the plurality of the firstbackground signals from the plurality of the first optical signals foreach of the plurality of the control samples, wherein the optimizing theplurality of the first background signals comprises subtracting theplurality of the first background signals from the plurality of thesecond optical signals received to obtain a mean baseline, wherein themean baseline corresponds to the second cycle number such that theplurality of the second optical signals corresponds to a predeterminedvalue; validating, using the processor, each of the plurality of thesecond optical signals against at least one of a plurality of referenceamplification curves; and computing, using the processor, the quantityof the target nucleic acid in the sample from the validated plurality ofthe second optical signals obtained as the function of the second cyclenumber for the target nucleic acid in the sample, wherein computing thequantity of the target nucleic acid in the sample from the validatedplurality of the second optical signals comprises performing an affinetransformation to apply at least one of a linear transformation and atranslation on the validated plurality of the second optical signals. 2.The method of claim 1, wherein the receiving the plurality of the firstoptical signals as the function of the first cycle number comprises:detecting the plurality of the first optical signals for each of theplurality of the control samples at each cycle of the firstamplification reaction, wherein each cycle of the first amplificationreaction corresponds to the first cycle number; and plotting theplurality of the first optical signals detected as the function of thefirst cycle number for each of the plurality of the control samples toobtain a first amplification curve, wherein the first amplificationcurve represents a ratio of each of the plurality of the first opticalsignals to a passive reporter dye optical signal as the function of thefirst cycle number.
 3. The method of claim 1, wherein the receiving theplurality of the second optical signals as the function of the secondcycle number comprises: detecting the plurality of the second opticalsignals for the target nucleic acid in the sample at each cycle of thesecond amplification reaction, wherein each cycle of the secondamplification reaction corresponds to the second cycle number; andplotting the plurality of the second optical signals detected as thefunction of the second cycle number for the target nucleic acid in thesample to obtain a second amplification curve, wherein the secondamplification curve represents a ratio of each of the plurality of thesecond optical signals to a passive reporter dye optical signal as thefunction of the second cycle number.
 4. The method of claim 1, whereinthe validating each of the plurality of the second optical signalsagainst the at least one of the plurality of the reference amplificationcurves comprises: generating at least the one of the plurality of thereference amplification curves, wherein the at least one of theplurality of the reference amplification curves comprises a plurality ofthird optical signals corresponding to a reference sample, wherein theat least one of the plurality of the reference amplification curvescomprises the plurality of the third optical signals corresponding to abackground region, an exponential growth region, and a plateau region;projecting each of the plurality of the second optical signals on to theat least one of the plurality of the reference amplification signals,wherein the projecting each of the plurality of the second opticalsignals on to the at least one of the plurality of the referenceamplification curves comprises determining whether each of the pluralityof the second optical signals obtained as the function of the secondcycle number for the target nucleic acid in the sample collapses on tothe at least one of the plurality of the reference amplification curves;and determining a threshold value for the plurality of the secondoptical signals projected on to the at least one of the plurality of thereference amplification curves.
 5. The method of claim 4, furthercomprising plotting the plurality of the second optical signalsprojected on to the at least one of the plurality of the referenceamplification curves to obtain a validated reference amplificationcurve.
 6. The method of claim 1, further comprising detecting theplurality of third optical signals for a plurality of amplicons, whereineach of the plurality of the third optical signals correspond to anoptical signal from at least one fluorescent dye.
 7. The method of claim1, wherein the linear transformation comprises scaling, and wherein thetranslation is selected from a group comprising a horizontal shift and avertical scaling.
 8. The method of claim 1, wherein the control sampleis an extraction blank.
 9. The method of claim 1, wherein the controlsample is a non-template control.
 10. The method of claim 1, wherein thevalidating each of the plurality of second optical signals against atleast one of a plurality of reference amplification curves comprises:generating the plurality of the reference amplification curves, whereineach of the plurality of the reference amplification curves comprises aplurality of third optical signals corresponding to a reference sample,wherein each of the plurality of the reference amplification curvescomprises the plurality of the third optical signals corresponding to abackground region, an exponential growth region, and a plateau region;projecting the plurality of the second optical signals onto theplurality of the reference amplification curves, wherein projecting theplurality of the second optical signals onto the plurality of thereference amplification curves comprises determining whether each of theplurality of the second optical signal obtained as the function of thesecond cycle number for the target nucleic acid in the sample collapseson to at least one of the plurality of reference amplification curves;and determining a threshold value for the plurality of the secondoptical signals projected on to the at least one of the plurality of thereference amplification curves.
 11. The method of claim 1, wherein thesample is a pre-amplified DNA sample.
 12. The method of claim 1, whereinthe sample is a pre-amplified RNA sample.
 13. The method of claim 1,further comprising normalizing the plurality of the first opticalsignals and the plurality of the second optical signals, whereinnormalizing the plurality of the first and the second optical signalscomprises determining a ratio of each of the plurality of the first andthe second optical signals to a passive reporter dye optical signal. 14.A method for determining a quantity of a target nucleic acid in asample, the method comprising: performing a first amplification reactionon a plurality of control samples; receiving a first amplification curverepresenting a plurality of first optical signals as a function of afirst cycle number for each of the plurality of control samples at eachcycle of the first amplification reaction, wherein the plurality of thefirst optical signals comprises a plurality of background signals;performing a second amplification reaction on the sample; receiving asecond amplification curve representing a plurality of second opticalsignals as a function of a second cycle number for the target nucleicacid in the sample at each cycle of the second amplification reaction;optimizing, using the processor, the plurality of the background signalsfrom the received plurality of first optical signals for each of theplurality of the control samples, wherein the optimizing the pluralityof the background signals comprises subtracting the plurality of thebackground signals from the plurality of the second optical signalsreceived to obtain a mean baseline, wherein the mean baselinecorresponds to the second cycle number such that the plurality of thesecond optical signals corresponds to a predetermined value; validating,using the processor, each of the plurality of second optical signalsdetected against a plurality of reference amplification curves, whereinvalidating each of the plurality of the second optical signalscomprises: receiving the plurality of the reference amplificationcurves, wherein each of the plurality of the reference amplificationcurves comprises a plurality of third optical signals corresponding to areference sample, wherein each of the plurality of the referenceamplification curves comprises the plurality of the third opticalsignals corresponding to a background region, an exponential growthregion, and a plateau region; projecting each of the plurality of thesecond optical signals on to the plurality of the referenceamplification curves; and determining a threshold for the plurality ofthe second optical signals projected onto at least one of the pluralityof the reference amplification curves; and performing, using theprocessor, an affine transformation on the validated plurality of thesecond optical signals to determine the quantity of the target nucleicacid in the sample, wherein the affine transformation comprises at leastone of a linear transformation and a translation.
 15. The method ofclaim 14, wherein the control sample is an extraction blank.
 16. Themethod of claim 14, wherein the control sample is a non-templatecontrol.
 17. The method of claim 14, wherein the projecting each of theplurality of the second optical signals on to the plurality of thereference amplification curves comprises determining whether each of theplurality of the second optical signal obtained as the function of thesecond cycle number for the target nucleic acid in the sample collapseson to at the least one of the plurality of the reference amplificationcurves.
 18. The method of claim 14, wherein the sample is apre-amplified DNA sample.
 19. The method of claim 14, wherein the sampleis a pre-amplified RNA sample.
 20. A system of determining quantity of atarget nucleic acid in a sample, said system comprising: a reactionchamber for performing a first amplification reaction on a plurality ofcontrol samples and a second amplification reaction on the sample; adetector for detecting a plurality of first optical signals as afunction of a first cycle number for the plurality of the controlsamples at each cycle of the first amplification reaction and aplurality of second optical signals as a function of a second cyclenumber for the target nucleic acid in the sample at each cycle of thesecond amplification reaction, wherein the plurality of the firstoptical signals comprises a plurality of background signals; and aprocessor comprising a memory for implementing program instructions of acomputer-readable medium, wherein said program instructions comprise:optimizing the plurality of the background signals from the receivedplurality of the first optical signals for each of the plurality of thecontrol samples, wherein the optimizing the plurality of the backgroundsignals comprises subtracting the plurality of the background signalsfrom each of the plurality of the second optical signals received toobtain a mean baseline, wherein the mean baseline corresponds to thesecond cycle number such that the plurality of the second opticalsignals correspond to a predetermined value; validating each of theplurality of the second optical signals detected against a plurality ofreference amplification curves, wherein the validating each of theplurality of the second optical signals comprises projecting each of theplurality of the second optical signals on to the plurality of thereference amplification curves to determine a threshold for theplurality of the second optical signals; and computing an initialquantity of the target nucleic acid in the sample from the validatedplurality of the second optical signals obtained as the function of thesecond cycle number for the target nucleic acid in the sample, whereincomputing the initial quantity of the target nucleic acid in the samplefrom the validated plurality of the second optical signals comprisesperforming an affine transformation on the validated plurality of thesecond optical signals, wherein the affine transformation comprises atleast one of a linear transformation and a translation.